advanced modeling - computer graphics research … · 2011-03-09 · 1 advanced modeling eduard...

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Advanced Modeling

Eduard Gröller, Thomas Theußl, Peter Rautek

Institute of Computer Graphics and Algorithms

Vienna University of Technology

Motivation

Real world phenomena

Complex geometry

Large deformations

Topological changes

Fuzzy objects

Tedious or impossible to model with meshes

Examples

Smoke, fire

Fluids

Fur, hair, grass

Eduard Gröller, Thomas Theußl, Peter Rautek 1

[http://physbam.stanford.edu/~fedkiw/]

Motivation



Motivation



Overview

Particle systems

Implicit modeling

Soft objects

Superquadrics

Level sets

Procedural modeling

Sweeps

Cellular texure generation

Terrain simulation

Vegetation simulation

Structure-deforming transformations


Particle Systems

Modeling of objects changing over time

Flowing

Billowing

Spattering

Expanding

Modeling of natural phenomena:

Rain, snow, clouds

Explosions, fireworks, smoke, fire

Sprays, waterfalls, lumps of grass


[Matthias Müller]

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Particle Systems - History

1982 Star Trek II: The Wrath of Khan


“A particle system is a collection of many many minute particles that together represent a fuzzy object. Over a period of time, particles are generated into a system, move and change from within the system, and die from the system.”

William T. ReevesParticle Systems - A Technique for Modeling a Class of Fuzzy Objects

ACM Transactions on Graphics, 1983

Particle Systems

Certain number of particles is rendered

Particle parameters change over time:

Location

Speed

Appearance

Particles die (lifetime) and are deleted


Particle Systems (2)

Particle shapes may be spheres, boxes, or arbitrary models

Size and shape may vary over time

Motion may be controlled by external forces, e.g. gravity


Particle Systems (3)

Particles interfere with other particles


Particle Systems: Bomb


Particle Systems: Grass Clumps


lifetime can be encoded by color: from green to yellow

3

Implicit Modeling

No fixed shape and topology

Modeling of Molecular structures

Water droplets

Melting objects

Muscle shapes

Shape and topology changeIn motion

In proximity to other objects


Implicit Modeling

No seams

Oriented surface (well defined inside and outside)

Differentiable

Closed

Continuous


Implicit Modeling

Implicit equation e.g.,

Vs. explicit equation e.g.,

Function

Right side constant (typically a threshold T)


Tyxyxf )(),( 22

n

2d function intersection with T - plane result (the 2d model)

The surface of an implicit model is defined as the set of points that fulfill the implicit equation

dkxy

Implicit Modeling

Level setslevel curve, iso contour, contour line

level surface, iso surface

level hypersurface

Changing the threshold

2

3

n


change of topology

Soft Objects: Blobs

Volume stays constant during movement

Molecular bonding: As two molecules move away from each other, the surface shapes

Stretch

Snap and finally

Contract into spheres


Definition of Blobby Objects

Sum of Gaussian density functions centered at the k control points

where

T is a specified threshold, and ak and bk adjust the blobbiness of control point k


k

rak Tebzyxf kk 0),,(

2

2222 )()()( kkkk zzyyxxr

),,( kkkk zyxX

4

Definition of Blobby Objects

Metaball model uses density functions, which drop off to 0 at a finite interval

Soft object model uses same approach with a different density-distribution characteristic


Superquadrics

Generalization of quadric representation

Additional parameters

Increased flexibility for adjusting object shapes

One additional parameter for curves and two parameters for surfaces


Superellipse

Exponent of x and y terms of a standard ellipse are allowed to be variable:

Influence of s:


1

/2/2

s

y

s

x r

y

r

x

Superellipsoid

Exponent of x, y and z terms of a standard ellipsoid are allowed to be variable:

Influence of s1 and s2:


11

1222 /2

//2/2

s

z

sss

y

s

x r

z

r

y

r

x

Procedural Modeling

High geometric complexity

Complex model does not exist as geometrySet of production rules


Demo Procedural Modeling

Motivation

One window in highest resolution ~7 million triangles

Modeled with 126 KB (18 KB zipped) of code

Changing parameters yields very different models


5

Sweeps

Modeling of objects with symmetries:Translational

Rotational

Represented by 2D shape

Sweep-path


Translational Sweeps

Control points of spline curve P(u)

Generates the solid, whose surface is described by point function P(u,v)


p1 p2

p0 p3P(u)

P(u,v)

Rotational Sweeps

Spline curve P(u)

Rotated about given rotation axis

Sampled at given angles yields the surface P(u,v)


rota

tion

axis

General Sweeps

Spline curve P(u)

Moved along a sweep path (e.g., spline)

Animated sweep path


[Kinetix 3D Studio MAX]

Sweeps - Pros and Cons

Advantages:Generates shapes that are hard to do otherwise

Disadvantages:Hard to render

Difficult modeling


Example


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Cellular Texture Generation

A cellular particle system, that changes geometry of surface

cell state

cell programs

extracellular environments


Cellular Texture Generation

Cell state: position, orientation, shape, chemical concentrations (reaction-diffusion)

Cell programs:

Go to surface, die if too far from surface, align, adhere to other cells, divide until surface is covered, ...

Differential equations

Extra cellular environment: neighbor orientation, concentration, ...



Cellular Texture Generation 2

Levels of Detail (LOD): Use fewer polygons for further distances

Cellular Texture Generation 3

Cell: group of polygons with texture and transparency maps


Cellular Texture Generation - Examples

Handling of unusual topologies

No problem with parameterization



Reaction-diffusion determine pattern of bumps and thorns


7


Cells (fur) oriented like their neighbors



Cells (fur) similarly oriented


Modeling and Visualization of Knitwear

Knitwear: simulation of thin 3D structure with instanced volume elements


basic element(R-loop)

basic element(L-loop)

Visualization of Knitwear

Volume element: 2D cross-section swept + rotated along parametric curve


x

y

p(t)

gg’

g"

b1b2

p0

p1

p2

p3

p4

p5

p6

C 1

C 2 C 3

C 4

x

y

z

z

x

p(t)

y g

Visualization of Knitwear

Rendering with raycastingSurface tiled with volumetric elements

Curved rays


xy

z

xm in xmax

viewing ray

top face

bottom face

Fu ,v

i jc

Pentry

cP

exit

Pp

entry

Pp

exit

y

z

x

’Pp

Pp

d

Pc’ u

w

v

Pc

d

Fu ,vi j

Knitwear - Examples


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Knitwear - Examples


Knitwear - Examples


Knitwear - Examples


Terrain Simulation

Fractals

Geographical Data

Simulations

Hybrids


Terrain Simulation Terrain Simulation

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Terrain Simulation Terrain Simulation

Terrain Simulation Realistic modeling and rendering of plant


Scene Synthesis System


Terrain


Height map Hills through noise synthesis

Stream through masking Water concentration (blue=high, yellow=low)

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Specification of Plant Populations

Space-occupancyExplicit specification (counting plants, painting)Procedural generation (cellular automata, reaction-diffusion)

Individual basedExplicit specification (survey, interactive specification)Procedural generation (point pattern generation model)


Self-thinning:Green: not dominated

Red: dominatedYellow: old

Distribution of eight species

Realistic Modeling and Rendering of Plants

Complex models necessary for realistic appearance

Plant distribution by ecosystem simulation and/or manual setting

Reduce geometric complexity by approximate instancing (similar plants, groups of plants or plant organs)

Parametrized models of individual plants


Plant Ecosystems - Examples








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Plant Ecosystems – Self Thinning


Plant Ecosystems – Self Thinning






Structure-Deforming Transformations

Non-linear transformationsTapering: non-linear scaling

Twist: non-linear rotation

Bend: also non-linear rotation


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Tapering

Scale factor is a function:


x

xf

xf

xf

x

z

y

x

)(00

0)(0

00)(

Twist

Angle of rotation is a function

e.g., for rotation about z-axis


xxfxf

xfxf

x

100

0)(cos)(sin

0)(sin)(cos

Bend

Also non-linear rotation


Example 1


Example 2


Other Topics not Covered Here

Shape grammars

Procedural architecture

Fractals (see Fraktale VO WS)


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Thank you for your attention

Questions?


References


advanced modeling - computer graphics research … · 2011-03-09 · 1 advanced modeling eduard...

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